Generalized framework for selectors with applications in optimal group testing

Annalisa De Bonis, Leszek Ga̧sieniec, Ugo Vaccaro

Research output: Chapter in Book/Report/Conference proceedingChapter

30 Scopus citations

Abstract

Group Testing refers to the situation in which one is given a set of objects script O sign, an unknown subset P ⊆ script O sign, and the task is to determine P by asking queries of the type "does P intersect Q?", where Q is a subset of script O sign. Group testing is a basic search paradigm that occurs in a variety of situations such as quality control in product testing, searching in storage systems, multiple access communications, and software testing, among the others. Group testing procedures have been recently applied in Computational Molecular Biology, where they are used for screening library of clones with hybridization probes and sequencing by hybridization. Motivated by particular features of group testing algorithms used in biological screening, we study the efficiency of two-stage group testing procedures. Our main result is the first optimal two-stage algorithm that uses a number of tests of the same order as the information theoretic lower bound on the problem. We also provide efficient algorithms for the case in which there is a Bernoulli probability distribution on the possible sets P, and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of "inhibitory" items in script O sign. Our results depend on a combinatorial structure introduced in this paper. We believe that it will prove useful in other contexts too.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsJos C. M. Baeten, Jan Karel Lenstra, Joachim Parrow, Gerhard J. Woeginger
PublisherSpringer Verlag
Pages81-96
Number of pages16
ISBN (Print)3540404937, 9783540404934
DOIs
StatePublished - Jan 1 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2719
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    De Bonis, A., Ga̧sieniec, L., & Vaccaro, U. (2003). Generalized framework for selectors with applications in optimal group testing. In J. C. M. Baeten, J. K. Lenstra, J. Parrow, & G. J. Woeginger (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 81-96). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2719). Springer Verlag. https://doi.org/10.1007/3-540-45061-0_8